We construct an effective “quantum force” to be used in the classical molecular dynamics part of the classical Wigner method when determining correlation functions. The quantum force is obtained by estimating the most important short time separation of the Feynman paths that enter into the expression for the correlation function. The evaluation of the force is then as easy as classical potential energy evaluations. The ideas are tested on three reaction rate problems. The resulting transmission coefficients are in much better agreement with accurate results than transmission coefficients from the ordinary classical Wigner method.

1.
E. J.
Heller
,
J. Chem. Phys.
65
,
1289
(
1976
).
2.
X.
Sun
and
W. H.
Miller
,
J. Chem. Phys.
106
,
916
(
1997
).
3.
R.
Hernandez
and
G. A.
Voth
,
Chem. Phys.
233
,
243
(
1998
).
4.
J. A.
Poulsen
,
G.
Nyman
, and
P. J.
Rossky
,
J. Chem. Phys.
119
,
12179
(
2003
).
5.
Q.
Shi
and
E.
Geva
,
J. Phys. Chem. A
107
,
9059
(
2003
).
6.
P.
Frantsuzov
,
A.
Neumaier
, and
V. A.
Mandelshtam
,
Chem. Phys. Lett.
381
,
117
(
2003
).
7.
D. C.
Marinica
,
M. -P.
Gaigeot
, and
D.
Borgis
,
Chem. Phys. Lett.
423
,
390
(
2006
).
8.
J. A.
Poulsen
,
G.
Nyman
, and
P. J.
Rossky
,
J. Phys. Chem. B
108
,
19799
(
2004
).
9.
J.
Liu
,
H.
Wang
, and
W. H.
Miller
,
J. Chem. Phys.
127
,
114506
(
2007
).
10.
J. A.
Poulsen
,
G.
Nyman
, and
P. J.
Rossky
,
J. Chem. Theory Comput.
2
,
1482
(
2006
).
11.
J. A.
Poulsen
,
G.
Nyman
, and
P. J.
Rossky
,
Proc. Natl. Acad. Sci. U.S.A.
102
,
6709
(
2005
).
12.
T. D.
Hone
,
J. A.
Poulsen
,
P. J.
Rossky
, and
D. E.
Manolopoulos
,
J. Phys. Chem. B
112
,
294
(
2008
).
13.
Q.
Shi
and
E.
Geva
,
J. Phys. Chem. A
107
,
9070
(
2003
).
14.
J.
Liu
,
H.
Wang
, and
W. H.
Miller
,
J. Chem. Phys.
128
,
144511
(
2008
).
15.
J. A.
Poulsen
,
J.
Scheers
,
G.
Nyman
, and
P. J.
Rossky
,
Phys. Rev. B
75
,
224505
(
2007
).
16.
J. A.
Poulsen
,
G.
Nyman
, and
P. J.
Rossky
,
J. Phys. Chem. A
108
,
8743
(
2004
).
17.
T. F.
Miller
 III
and
D. E.
Manolopoulos
,
J. Chem. Phys.
123
,
154504
(
2005
).
18.
J.
Lobaugh
and
G. A.
Voth
,
J. Chem. Phys.
106
,
2400
(
1997
).
19.
T.
Yamamoto
,
H.
Wang
, and
W. H.
Miller
,
J. Chem. Phys.
116
,
7335
(
2002
).
20.
J.
Shao
,
J. -L.
Liao
, and
E.
Pollak
,
J. Chem. Phys.
108
,
9711
(
1998
).
21.
H.
Wang
,
X.
Sun
, and
W. H.
Miller
,
J. Chem. Phys.
108
,
9726
(
1998
).
22.
W. H.
Miller
,
J. Chem. Phys.
61
,
1823
(
1974
).
23.
R. P.
Feynman
and
A. R.
Hibbs
,
Quantum Mechanics and Path Integrals
(
McGraw-Hill
,
New York
,
1965
).
24.
S.
Jang
and
G. A.
Voth
,
J. Chem. Phys.
112
,
8747
(
2000
).
25.
26.
I. R.
Craig
and
D. E.
Manolopoulos
,
J. Chem. Phys.
122
,
084106
(
2005
).
You do not currently have access to this content.